Spin hamiltonian for which quantum hall wavefunction is exact

Abstract

Abstract A Hamiltonian is introduced for which the spin- 1 2 quantum liquid wavefunction proposed by Kalmeyer and Laughlin is the exact ground state. An explicit proof is given that this state is a doubly degenerate spin singlet. The excitation spectrum of the Hamiltonian is calculated variationally and a case is made for the presence of an energy gap. The spin-1 collective mode, calculated in the single-mode approximation, is shown to have a large energy that is minimized at the Brillouin zone corner. The spin-0 collective mode behaves similarly but has a lower overall energy. Wavefunctions for the neutral spin- 1 2 excitations are shown to form an exact spin doublet. The energy of a pair of such excitations increases or decreases logarithmically with separation depending on the total spin. When widely separated, the excitations possess an internal 2-fold degree of freedom, a Brillouin zone that is half the linear dimension of the full zone, and a mass comparable to that of the collective modes.

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